What is log_{3}((xsqrt(x-1))/2) ?

The solution to log_{3}((xsqrt(x-1))/2) is log_{3}(x)+log_{3}(sqrt(x-1))-log_{3}(2)

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simplify log_{3}((xsqrt(x-1))/2)

simplify

lo g_{3} (\frac{x x - 1}{2})

lo g_{3} (x) + lo g_{3} (x - 1) - lo g_{3} (2)

Solution steps

lo g_{3} (\frac{x x - 1}{2})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{3} (\frac{x x - 1}{2}) = lo g_{3} (x x - 1) - lo g_{3} (2)

= lo g_{3} (x x - 1) - lo g_{3} (2)

Simplify

lo g_{3} (x x - 1) : lo g_{3} (x) + lo g_{3} (x - 1)

= lo g_{3} (x) + lo g_{3} (x - 1) - lo g_{3} (2)

lo g_{10} (23 c d)

lo g_{e} (\frac{4}{5})

lo g_{8} (9) + lo g_{8} (11)

5 lo g_{7} (v) + 10 lo g_{7} (w) - \frac{lo g _{7} ( u )}{5}

What is log_{3}((xsqrt(x-1))/2) ?
The solution to log_{3}((xsqrt(x-1))/2) is log_{3}(x)+log_{3}(sqrt(x-1))-log_{3}(2)